From single-particle to many-body mobility edges and the fate of overlapped spectra in coupled disorder models

Mobility edge (ME) has played an essential role in disordered models. However, while this concept has been well established in disordered single-particle models, its existence in disordered many-body models is still under controversy. Here, a general approach based on coupling between extended and localized states in their overlapped spectra for ME is presented. We show that in the one-dimensional (1d) disordered single-particle models, all states are localized by direct coupling between them. However, in $d \ge 2$ disordered single-particle and 1d disordered many-body models, the resonant hybridization between these states in their overlapped spectra makes all states be extended, while these in the un-overlapped spectra are unchanged, leading to tunable MEs. We propose several models, including two disordered many-body spin models, to verify this mechanism. Our results establish a unified mechanism for MEs and demonstrate its universality in single-particle and many-body models, which opens an intriguing avenue for the realization and verification of MEs in many-body localization.